Simulating the Structure and Dynamics of Heterogenous Nanoclusters François G. Amar Department of Chemistry University of Maine Department of Chemistry & Physics, UNE January 23, 2009

Acknowledgements Jinasena Hewage (now at University of Ruhuna) James Smaby TJ Preston Gérard Torchet & Marie-Françoise de Feraudy Marcus Lundwall & Swedish group at Lund

Motivation Interested in how material properties vary as system size grows from atom to bulk. Novel or special properties of ultra-small chunks of matter: catalysis, transport, fabrication. Varying the stoichiometry as well as size of small particles adds another “tunable” parameter. Finite heterogeneous systems are also of intrinsic interest.

Ballistic deposition of Cu on Ag yields subsurface shells: ”onion” (MD with embedded atom potentials) At intermediate temperature fcc-A-core supports A-B-A growth while ico-A-core does not. F. Balleto, C. Mottet, and R. Ferrando, PRL 90(13) 5504 (2003)

Molecular Beam Source Ar P=1 bar T=300 K V=550 m/s

A Closer Look at the Beam V=550 m/s  v s =13 m/s In skimmed beam, T ~ 0.5 K Mach # = V/ v s ~ 40

How do we know what clusters are predominant in the jet? Sizes Structure Stoichiometry

Perform experiments! V=550 m/s  electron diffraction 10 millisecond time window! h UV-vis or IR spectrum ionizing e- beam mass spectrum

Notice maxima at rare gases

Why is mercury a metal? When does it become so? Recall, Hg: [Xe] (4f) 14 (5d) 10 (6s) 2 Let’s look at that ionization energy again. HgHg (l) 10.3 eV 4.49 eV Hg n ?

Rademan, Kaiser, Even, Hensel, PRL 59, 2319 (1987)

Around n=20, change in slope suggests transition from van der Waals to metallic behavior 1/R ~ 1/n 1/3

What about the theory of these small objects? Structure ab initio quantum mechanics or DFT (for smaller clusters) Semi-empirical quantum theory Empirical force-fields or potential energy surfaces van der Waals systems larger clusters PES from scattering experiments…

Dynamics Quantum dynamics (9 degrees of freedom) Quantum MD (classical MD with forces from DFT) aka Car-Parrinello Classical dynamics on potential energy surfaces Large clusters Long times: 10 nanoseconds! Solve:

Thermodynamics Path integral Monte Carlo; diffusion MC Multiple histogram methods using classical dynamics on potential energy surfaces ; adiabatic switching accurate classical densities of states (“heavy” atoms) larger clusters

Two recent projects from our group Ar/N 2 cluster structure and dynamics Simulating the photoelectron spectra of Ar n, Xe n, Ar n Xe m clusters

Two recent projects from our group Ar/N 2 cluster structure and dynamics Simulating the photoelectron spectra of Ar n, Xe n, Ar n Xe m clusters

V(r) for Ar 2

Ar/N 2 Potential Models Ar-Ar (Aziz-Chen 4 ) R e =3.75 Å; D e =99.4 cm -1 N 2 -N 2 (exp charge quadrupole 2 ) Canted parallel: R e =3.98 Å; D e =102.5 cm -1 T-shape: R e =4.15 Å; D e =102.8 cm -1 Ar-N 2 (damped dispersion model fit to ab initio 3 ) R e =3.64 Å; D e =111.9 cm -1

Ar 7 (N 2 ) 6 with Ar at center Despite the stronger pair interaction, N 2 appears to be less easily incorporated into the center of the cluster than Ar due to frustration effects. Ar 7 (N 2 ) 6 with N 2 at center

Ar centered N 2 centered The Caloric Curve: Heat both the Ar-centered and N 2 -centered isomers Inflection is a signature of “melting”

Caloric curve RMS bond fluctuation parameter Orientational order parameter

What does melting mean away from the thermodynamic limit (large N)? TmTm E TmTm N --> ∞ E TmTm TmTm small N

T / K Ar-centered clusters

N 2 -centered clusters

t = 255 ps t = 0 ps t = 5 ps t = 450 ps t = 500 ps N 2 molecules mix throughout cluster and migrate to surface (N 2 ) 13 Ar 42 Dynamics Initial structure: quenched cuboctahedron with N 2 in center T = 41 K (liquid-like)

Two recent projects from our group Ar/N 2 cluster structure and dynamics Simulating the photoelectron spectra of Ar n, Xe n, Ar n Xe m clusters

“Phase” diagram of A 55 B 55 :  =  AB /  AA  =  BB /  AA A.S. Clarke, R. Kapral, and G.N. Patey, JCP 101, 2432 (1994)

What does the photoelectron experiment measure? So… …calculate the final state polarization energy (the signal electrons--at 50 eV--leave in seconds)

Potentials DimerR e / ÅD e / K Ar-Ar a Ar-Xe b Xe-Xe a a Slavicek et al, JCP 119, 2102 (2003) b Aziz et al, JCP 78, 2402 (1982) HFD type potentials with accurate well depths and equilibrium bond lengths. Cubic splines used for potential and force.  =0.72  =0.54

Making clusters Start with perfect ordered structures such as icosahedra and then warm and anneal within a bounding sphere. Xe 300 ico 0 pdp 5 hcp 67 fcc 52 unknown 176

The induced dipoles are iterated to self-consistency, taking about 6 to 8 iterations to achieve self-consistent energies to 1 part in The polarization energies are binned to construct a histogram and we typically average over an ensemble of 10 to 20 clusters. [  Xe =4.04Å 3 ;  Ar =1.64Å 3 ] Polarization energy calculation Self-consistent polarization energy calculation in which each atom in a cluster takes the role of the ion

Pure Xenon “4d 5/2 ” Xe 150 Xe 1000 Xe 500 Xe 250 Pure Argon “2p 3/2 ” Ar 150 Ar 250 Ar 500 Ar 1000

Signal Attenuation  r d R

What is the mean free path? Dependent on material and electron kinetic energy. Tchaplyguine et al, permit an estimate of: =17 Å and 9 Å for Xe and Ar clusters, respectively for 50 eV signal electrons. Alternatively, the TPP-2M formula gives (IMFP) Xe  6.5 Å and Ar =10.9 Å at the same energy. We use Xe  6.5 Å and Ar =9 Å in the following.

Broadening Convolute screened histogram data with Voight profile of isolated atom signal provided by experimentalists Atom h  /eV KE el / eVFWHM / eV Xe120~ Ar310~

Simulated Xe 4d 5/2 spectrum Structure in the raw histogram bulk peak reflects local environment but is no longer apparent after broadening. For Xe 309, screening tends to “reduce” the bulk peak. Xe 309 “raw” Xe 309 broadened Xe 309 screened broadened

Pure Ar cluster spectra at 50 eV ( =9Å) Exp: ≈300 Ar 500 Ar 250 Ar 1000

Pure Xe spectra Exp: =900 Xe 150 Xe 250 =17Å Xe 500 Exp: =900 Xe 500 =6.5Å Xe 250 Xe 1000

The polarization shift calculation appears to give semi-quantitative shifts 1)Experimentalists report a Gaussian size distribution in their beam with a FWHM =. 2) Point dipole model may be inadequate. 3) Thermal treatments may affect final spectrum

Mixed Clusters

Experimental data* *Thanks to to M. Lundwall for sharing these results prior to publication.

Xe 500 Ar 500 core/shell structure Xe spectrum Ar spectrum

1) SubstituteAr atoms with single Xe atoms (“pepper”) Substitute Ar atoms with small clusters of Xe (“plum”) Modified clusters Start with Xe/Ar core-shell.

Xe 1000 Xe 396 Ar 527 “plum”

Ar 250 Xe 396 Ar 527 “plum”

Conclusions Polarization energy shift model captures the essential physics and is quantitative to within about 5%. The bulk/surface shift model for pure clusters of Tchaplyguine et al is well supported by our atomistic calculations. Our preliminary calculations of mixed clusters supports the layering model proposed by the Swedish group. As the Ar/Xe ratio in the beam increases it appears that the cluster will consist of a core/shell structure with trapped Xe atoms and/or small clusters in the outer Ar layer.

Continuing Work TJ Preston is refining the pure Ar and Xe cluster simulations and will be tackling the mixed cluster problem for his thesis.

FIN

Xenon spectrum of mixed clusters ( Xe =6.5 Å; Ar =9 Å)

Argon spectrum of mixed clusters ( Xe =6.5 Å; Ar =9 Å)

Xe 396 Ar 527 raw “plum” Xe 396 Ar 527 screened Xe 374 Ar 549 raw “pepper” Xe 374 Ar 549 screened Xe 396 Ar 527 raw “plum” Xe 396 Ar 527 screened Xe 374 Ar 549 raw “pepper” Xe 374 Ar 549 screened Xenon spectrumArgon spectrum

Making clusters I Start with perfect ordered structures such as icosahedra and then warm and anneal. Xe 300 (initially a cuboctahedron): ico 0 pdp 0 hcp 58 fcc 71 unknown 171

Making clusters II Grow from a small seed by bombarding with monomers while annealing (velocity scaling) within a bounding sphere. Xe 300 ico 0 pdp 5 hcp 67 fcc 52 unknown 176

TPP-2M formula RGIMFP/Å EE  /Å M/g-mol -1 r/g-cm -3      Ar Xe

Compare single cluster spectrum with spectrum of a size distribution N% Xe 309 and Xe ensemble spectra: =6.5 Å

Polarization models (Böttcher) Consider an ion (1) and a neutral (2) a distance s apart: s a

Ratio of homogeneous and point polarization energies W h /W p s/a ReRe

What does theory already say about mixed rare gas clusters? L. Perera and F. G. Amar, JCP 93, 4884 (1990). Garzon et al studied A 13 B 13 systems (1989). Single guest/host systems: Scoles, LeRoy, FGA, … Xe in Ar (Scharf, et al)

What is the mean free path, ? Dependent on material and electron kinetic energy. Tchaplyguine et al, permit an estimate of: Xe = 17 Å and Ar = 9 Å for 50 eV signal electrons. We use these values in the calculations presented here.

Swedish experiments/data

Pure Ar cluster spectra at 50 eV ( =9Å) ≈300 Ar 150 Ar 250 Ar 500

Simulated Xe 4d 5/2 spectrum Structure in the raw histogram bulk peak reflects local environment but is no longer apparent after broadening. For Xe 309, screening tends to “equalize” the two peaks.

Experimental data on Mixed clusters

Experimentalists report a Gaussian size distribution in their beam with a FWHM =. N% Compare Xe 309 and Xe ensemble spectra: =17Å

X50Ar200 --> Xe =17 Å

L=6.5

Pepper

Plum

Xe 396 Ar 527 raw “plum” Xe 396 Ar 527 screened Xe 374 Ar 549 raw “pepper” Xe 374 Ar 549 screened Modified clusters Start with Xe/Ar core- shell cluster (XeAr), then: 1)Substitute Ar atoms with small clusters of Xe (“plum”) 2)2) SubstituteAr atoms with single Xe atoms (“pepper”)